Dear all, I have a system of equations to solve, which involves three space dependent functions phi, eta, lambda and two constants/scalars Z, W. These need to be solved simultaneously because all the equations involve at least 2 unknowns. How do I solve that, considering that one of the scalar equations includes a spacial integral of one of the (still unknown) functions? Is it best to define the scalars as Constants? This problem goes away when I write down the system in a standard FEM formulation, introducing the mass matrix etc. In this case, it is clear that I could solve for that function and then consecutively solve each of the remaining 4 equations. It is not that obvious how I can do that using Firedrake, that is why I thought I would have to solve simultaneously, but then I have the problem described above. Regards, Anna. On 06/08/15 11:04, Lawrence Mitchell wrote:

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Hi Anna,

On 06/08/15 10:37, Anna Kalogirou wrote:

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Dear all,

I have a rather simple question but I would like to get some feedback from someone in the Firedrake team.

I am now working on the problem which includes solving a variational problem in a part of the domain only (a water wave problem which includes a floating body).

I can think of a couple of possible solutions on how to solve this: 1. Define two domains and solve the problem separately in each domain. However, I will have to deal with nonzero boundary conditions on the common boundary.

2. I prefer solving the problem in the whole domain, since most of the equations/functions are valid everywhere. Then I can define a Heavyside step function which will be 0 in one part and 1 in the part of the domain I am interested in (under the floating body). I will essentially write down a variational problem valid everywhere, but will actually be zero in a part of the domain.

Is the 2nd step a good approach? The question essentially is how to split a mass matrix M_kl which is defined everywhere, and solve and integral form in a part of the domain only. I think step two is a fine approach. However, note the following issues at present. The way you would have to do this currently is as follows:

Define a DG0 field to hold your indicator function

indicator = Function(DG0)

# Set it to 1 in the appropriate part of the domain indicator.interpolate(...)

# Now use this extra field everywhere when defining your variational # problem.

However, all your integrals are still over the whole domain, you just pick up lots of zeros.

Steadily climbing our todo list (and at an increasing pace, I feel), is the ability to define proper sub domains in a mesh, and then be able to perform integrals over them. Until that time, I think approach 2 is somewhat easier to do than approach 1.

Cheers,

LAwrence -----BEGIN PGP SIGNATURE----- Version: GnuPG v1

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